However, using non-interacting GREEN's function in self-energies, which is referred to as BORN approximation, is not fully consistent, since the background particles contributing to the self-energy are treated as non-interacting. In reality, of course, these particles also move in an average potential coming from the presence of all the other particles. Thus instead of non-interacting GREEN's functions (single lines), one has to use the exact GREEN's function (double line) in the proper self-energy, as shown in Fig. 3.9. Since the exact GREEN's function both determines and is determined by the proper self-energy , this approximation is known as the self-consistent BORN approximation (see Appendix F.3). The self-consistent approach preserves conservation laws (Appendix F.3), for example, the continuity equation holds valid (Section 3.9.4). Throughout this work the self-consistent BORN approximation is applied.